GLOBAL ATTRACTORS FOR DAMPED SEMILINEAR WAVE EQUATIONS

By J. Ball. 2003

491 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1267f7f3fae528509a46398a46207b000555229b

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In Applied Mathematics

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Citations in the corpus

Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R 3 (2005, unknown): “, [10,11]) depends on the weak continuity of relevant energy functionals.”
Attractors for reaction-diffusion equations in R N with continuous nonlinearity (2005, methodology): “To avoid this problem the method of the energy equation, which has been successfully used in many papers for equations with uniqueness of solutions (see, for example, [21,28,34,35,42,46]) and also for a wave equation without uniqueness [7], is an appropriate tool.”
Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, methodology): “Notice that the compactness of the embeddings H(1)(Q) ↪→ L(Q) with p < 6 was crucial and frequently used in [4] when Q is bounded.”
On global attractors of the 3D Navier-Stokes equations (2006, background): “Now, passing to a subsequence and dropping a subindex, we obtain that there exists u ∈ E([0,∞)), such that un → u in C([0, 2];Hw) as n → ∞.”
Global solutions and finite time blow up for damped semilinear wave equations ? ? The first author w (2006, background): “MSC:35L70; 35B40 Keywords:Damped wave equations; Stable and unstable set; Global solutions; Blowing up solutions; Convergence to equilibria; Neh manifold; Mountain pass level”
Attractors for differential equations with unbounded delays (2007, methodology): “Opposite to the second case in the above paragraph, in this section we will prove in a different way with less restrictive conditions that it is possible to obtain boundedness for the semigroup associated to an autonomous infinite delay differential equation, combining the ideas from Wang & Xu [30] ”
Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains (2008, methodology): “The energy equation method was developed by Ball in [9, 10] and used by many authors (see, e.”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, methodology): “This method was applied with success to many equations, both in bounded and unbounded domains, see [24,34,63,110,113–115,125,126,148,180–182,198,199,217,226– 228], and [229].”